Chaboche Viscoplastic Model Research Articles

Thermo-mechanical fatigue analysis of ferritic stainless steel STS444LM for exhaust manifold application

This work presents thermo-mechanical fatigue (TMF) life analysis of ferritic stainless steel STS444LM recently developed to enhance the durability of the automotive exhaust manifolds. To determine cyclic material properties, isothermal tensile and low cycle fatigue (LCF) tests at temperature ranging from 200 °C to 900 °C under two different strain rates of 0.1 %/s and 0.01 %/s are performed. Based on these tests, the unified Chaboche visco-plasticity model is determined. Then, the TMF test using the V-shaped specimen subjected to the temperature cycle from 250 to 850 – 950 °C with three different dwell times at the maximum temperature is performed. An energy-based model based on the Morrow model is determined using TMF test data by incorporating effects of the dwelling time and maximum temperature.

An Overview of the mechanism-based thermomechanical fatigue method (DTMF) in the design of automotive components

The DTMF damage Parameter described in the paper is the generalization of the creep fatigue parameter (DCF) proposed by Riedel, which quantifies the amount of damage produced by a non-isothermal loading cycle. The entire design methodology is outlined in the text, starting with the calibration of Chaboche's viscoplastic model and then the determination of the thermomechanical fatigue (TMF) parameters. Chaboche is generally a good choice for its ability to describe well both kinematic and isotropic hardening behaviors, also enabling stress relaxation and strain rate dependency to be considered. The DTMF method is based on the fracture mechanics concept of cyclic crack tip opening displacement (ΔCTOD) where the effective stress range takes the crack closure effect into account. This method is typically used to describe the thermomechanical low cycle fatigue behavior of cast irons, cast steels, stainless steels, Inconel, HiSiMo and nickel-based alloys. These materials are used in components that need to withstand high temperatures (higher than half of the melting point) in service as exhaust manifolds, cylinder heads, valves, turbochargers and disk brakes. Three failure mechanisms are detailed here: oxidation, creep and fatigue. Oxidation is a complex phenomenon that may occur when the material is hot under tensile in-phase loading or hot under compressive out-of-phase loading. Creep is a time and temperature dependent diffusion process which is incorporated into the DTMF parameter as a multiplicative factor. In this context fatigue life is defined as the number of cycles to propagate an existent microcrack up to an arbitrary size that is defined on a case-by-case basis.

Experimental investigation and constitutive material modelling of low cycle fatigue of EUROFER97 for fusion applications

EUROFER97 is one of the candidate materials for structural components of fusion nuclear reactors (i.e. ITER and DEMO). Due to the plasma instabilities and cyclic operating conditions, these structural components are expected to face asymmetric thermomechanical fatigue loading. In this work, existing models based on the Chaboche viscoplasticity model have been modified in order to represent the fatigue behaviour of EUROFER97 under different strain ratios and ranges. The modified model has been parameterized based on experimental data obtained from fatigue tests of EUROFER97, in which the strain range varied from 0.6 % to 1.5 % and the strain ratio was either -1 or 0 at room temperature or 350 °C. The incorporation of the strain memory effect into the isotropic hardening due to the observed non-Masing behaviour of EUROFER97 enabled the use of unified parameters for every temperature that could cover all the different testing conditions. In order to validate the current model, the simulated results are compared to strain controlled low cycle fatigue test data performed at room temperature and 350 °C, which were not used for the parameterization. A good match between the simulation and experimental results proves the predictive capability of the proposed modified model.

Physics-Based Self-Learning Recurrent Neural Network enhanced time integration scheme for computing viscoplastic structural finite element response

In the current study, we present an application to the class of deep learning known as the Physics Informed Neural Networks (PINNs), more specifically we develop a new implicit material integration scheme based on Recurrent Neural Network (RNN). In this study, we refer to it as the Recurrent Enhanced Implicit Integration Scheme (REIIS). We illustrate how to incorporate the constitutive relations into REIIS and explore its application to Lemaitre–Chaboche viscoplastic model. Whilst common applications in this class of deep learning utilize feed-forward neural networks (FFNN) for training, we propose a combination of the Long Term Short Memory (LSTM) network with FFNNs for an accurate representation of the state variables. Furthermore, with the present strategy, we combine the data-driven approach of replacing the material behavior with NN along with its ability to learn continuously through physical laws. To validate the approach, we test the results of the framework with the numerical solution obtained with Finite Element Method (FEM) for Reissner–Mindlin plate elements at different strain rates. We further observe that obeying physical constraints leads to improved robustness in the learning of REIIS and broadens the scope of integrating the NNs in FEM.

A viscoelastic-viscoplastic constitutive model for high-temperature response of an advanced steel verified by biaxial measurement experiments

This paper presents a viscoelastic-viscoplastic constitutive model for representing different aspects of the high-temperature deformation response of advanced martensitic steel. The model decomposes the strain into three components of elastic, viscoelastic, and viscoplastic. The elastic behaviour is represented by Hooke's law; 2 K-Voigt models in series are used for the viscoelastic response, and a variant of the two back-stress terms Chaboche model is employed for the viscoplastic part. The effectiveness of the proposed model has been examined for representing the deformation behaviour of a 10%Cr martensitic steel at 600 °C. It has been shown that the developed model provides a sufficiently accurate description of i) constant-load creep after various prior loadings, ii) constant-strain stress-relaxation, iii) anelastic recovery, and iv) negative creep behaviour of the 10%Cr steel. The model results are compared with those from a three back-stress terms Chaboche viscoplastic model to indicate the importance of considering the viscoelastic component. Furthermore, observations from biaxial measurements of axial and radial deformation for a uniaxially loaded testpiece were used to demonstrate the necessity of considering the viscoelastic contribution for accurately representing the high-temperature deformation response of steels.

Ratcheting response of spherical vessels under load-controlled condition based on the Chaboche viscoplastic model

Ratcheting response of spherical vessels under load-controlled condition based on the Chaboche viscoplastic model

Chaboche's Viscoplasticity Model for Strain – Space Plasticity

To obtain reliable stress and strain fields using finite-element simulations, the applied constitutive equations, in general formulated in terms of evolution equations for the stresses and a set of state variables, that should be able to describe hardening properties as well as micro structural aspects with sufficient accuracy. The viscoplastic response of materials requires the time integration of system of non-linear first order differential equations. In viscoplasiticy, the constitutive equation might become very complicated to evaluate depending upon their degree of non-linearity. The constitutive model includes a yield criterion and multi-component formulations of non-linear isotropic and kinematic hardening. Both the types of the loading and the complexity of the constitutive laws ask a stable and efficient algorithm. The elasto-viscoplastic constitutive equations of the Chaboche model have been developed and modified many times. In this study Chaboche viscoplastic constitutive model is presented in strain-space. This model is further implemented in the framework of finite element. The performance of the new algorithm is compared to that is presented in existing literature results.

Testing, characterization and modelling of mechanical behaviour of poly (lactic-acid) and poly (butylene succinate) blends

Abstract Background Significant amount of research, both experimental and numerical, has been conducted to study the mechanical behaviour of biodegradable polymer PL(L)A due to its wide range of applications. However, mechanical brittleness or poor elongation of PL(L)A has limited its applications considerably, particularly in the biomedical field. This study aims to study the potential in improving the ductility of PLA by blending with PBS in varied weight ratios. Methods The preparation of PLA and PBS blends, with various weight ratios, was achieved by melting and mixing technique at high temperature using HAAKE™ Rheomix OS Mixer. Differential Scanning Calorimetry (DSC) was applied to investigate the melting behaviour, crystallization and miscibility of the blends. Small dog-bone specimens, produced by compression moulding, were used to test mechanical properties under uniaxial tension. Moreover, an advanced viscoplastic model with nonlinear hardening variables was applied to simulate rate-dependent plastic deformation of PLA/PBS blends, with model parameters calibrated simultaneously against the tensile test data. Results Optical Microscopy showed that PBS composition aid with the crystallization of PLA. The elongation of PLA/PBS blends increased with the increase of PBS content, but with a compromise of tensile modulus and strength. An increase of strain rate led to enhanced stress response, demonstrating the time-dependent deformation nature of the material. Model simulations of time-dependent plastic deformation for PLA/PBS blends compared well with experimental results. Conclusions The crystallinity of PLA/PBS blends increased with the addition of PBS content. The brittleness of pure PLA can be improved by blending with ductile PBS using mechanical mixing technique, but with a loss of stiffness and strength. The tensile tests at different strain rates confirmed the time-dependent plastic deformation nature of the blends, i.e., viscoplasticity, which can be simulated by the Chaboche viscoplastic model with nonlinear hardening variables.

Multiaxial Viscoplasticity Modelling of Power Plant Steel

The thermo-mechanical fatigue (TMF) of power plant components is caused by the cyclic operation of power plant. A time-dependent plasticity model can be used to simulate the component response under cyclic thermo-mechanical loading. This paper is concerned with the modelling of thermo-mechanical behaviour of power plant steel under various loading conditions. Fully-reversed, strain-controlled tests were conducted on a parent material of P91 steel at high temperatures in order to determine material constants. A unified, Chaboche viscoplasticity model, was used to model the TMF behaviour of the steel. The multiaxial form of the Chaboche constitutive equations have been implemented in the finite element software and validated by comparing to experimental data. Simulation results have been compared with the results of anisothermal cyclic testing in order to validate the performance of the model in cyclic temperature conditions. The model’s performance under multiaxial stress conditions was investigated by testing and simulating the notched bar specimen under load-controlled conditions.

The application of modified viscoplastic constitutive relationship on the warpage prediction of injection-molded part

It is important to have an accurate description of the mechanical behavior of polymer when predicting the warpage of injection-molded part. The viscoplastic model for polymer was developed based on the classical Chaboche viscoplastic model for polycrystalline metals. The cyclic tensile test was performed at three levels of strain rate and six levels of temperature. The ratio between Young’s modulus in the unloading and loading path was described as function of total strain. The warpage prediction for a plaque has been conducted successfully. The simulated deflection has a good agreement with the measured one by the viscoplastic model for polymer. It also exhibits a significant improvement compared with the simulated one by viscoplastic model for polycrystalline metals.

Pragmatic optimisation methods for determining material constants of viscoplasticity model from isothermal experimental data

A procedure to estimate material constants for the unified Chaboche viscoplasticity model from experimental data has been published elsewhere; however several critical assumptions are made to enable this and potential numerical problems can limit the effectiveness of the optimisation. Pragmatic optimisation procedures are therefore required to determine the material properties accurately and efficiently. This is made more complex by the presence of several deformation mechanisms and their interactions. Automation is critical due to the large amounts of data generated in testing. Complications that inhibit this process can arise due to factors such as experimental scatter. In this paper, a general optimisation framework is discussed and investigated using data from isothermal tests on a P91 steel at 600°C. Potential obstacles in the procedure are addressed and solutions (such as pre-optimisation experimental data ‘cleaning’) are suggested. Methods to maximise the amount of confidence a user has in a particular optimised constant set are also discussed.

Comparison of several optimisation strategies for the determination of material constants in the Chaboche visco-plasticity model

Determining representative material constant sets for models that can accurately predict the complex plasticity and creep behaviour of components undergoing cyclic loading is of great interest to many industries. The Chaboche unified visco-plasticity model is an example of a model that, with the correct modifications, shows much promise for this particular application. Methods to approximate material constant values in the Chaboche model have been well established; however, the need for optimisation of these parameters is vital due to assumptions made in the initial estimation process. Optimisation of a material constant set is conducted by fitting the predicted response to the experimental results of cyclic tests. It is expected that any experimental data set (found using the same values of test parameters such as temperature; the dependency of which is not accounted for in the original Chaboche model) should yield a single set of optimised material parameters for a given material. In practice, this may not be the case. Experimental test programs usually include multiple loading waveforms; therefore, it is often possible to optimise for separate, different sets of material constants for the same material operating under comparable conditions. Several optimisation strategies that utilise multiple sets of experimental data to form the objective functions in optimisation programs have been applied and critiqued. A procedure that evaluates objective functions derived from the multiple experimental data types simultaneously (i.e. in the same optimisation iteration) was found to give the most consistently high-quality fitting. In the present work, this is demonstrated using cyclic experimental data for a P91 steel at 600 °C. Similar strategies may be applied to many constitutive laws that require some form of optimisation to determine material constant values.

Thermal-mechanical fatigue simulation of a P91 steel in a temperature range of 400–600°C

This paper deals with the identification of material constants to simulate the effect of cyclic mechanical loading and temperatures. A Chaboche viscoplasticity model was used in this study to model the thermal-mechanical behaviour of a P91 martensitic steel. A fully-reversed cyclic mechanical testing programme was conducted isothermally between 400 and 600°C with a strain amplitude of 0.5%, to identify the model constants using a thermo-mechanical fatigue (TMF) test machine. Thermo-mechanical tests of P91 steel were conducted for two temperature ranges of 400 – 500°C and 400 – 600°C. From the test results, it can be seen that the P91 steel exhibits cyclic softening throughout the life of the specimens, for both isothermal and thermal-mechanical loading and this effect can be modelled by the set of viscoplasticity constants obtained. Finite element simulations of the test specimens show good comparison to isothermal and TMF experimental data.

Cyclic softening behaviour of a P91 steel under low cycle fatigue at high temperature

This paper describes a model used to represent the cyclic mechanical behaviour of P91 martensitic steel. Low cycle fatigue tests were conducted at 600°C using a thermo-mechanical fatigue test machine. A unified, Chaboche viscoplasticity model, was used to model the behaviour of the steel. The micro structure of the steel at different life fractions of the tests was investigated using scanning and transmission electron microscope images. The viscoplasticity model, with two stages of softening period, has resulted in better prediction capability for the cyclic behaviour of the steel for an initially undamaged material prior to crack initiation.

Modelling of Damage Development and Strain Ratchetting Using a Viscoplastic Constitutive Formulation

Simulation of both damage development and strain ratchetting in uniaxial loading conditions has been presented for a nickel-based superalloy at 650°C using the unified Chaboche viscoplastic model. A third kinematic hardening component was employed to simulate strain ratchetting; and a damage variable, based on plastic strain development, was also incorporated to simulate the damage evolution behaviour. Good agreement between the model predictions and the experimental results was obtained for both damage evolution and strain ratchetting. The model was then utilised to investigate the cyclic deformation behaviour near a crack tip for a single edge notch tension (SENT) specimen. Finite element analyses showed that strain ratchetting is seems to be a characteristic of the fatigue crack tip, which has been used as a criterion to predict the crack growth rates.

Unified viscoplastic models for low cycle fatique behavior of Waspaloy

The deformation behavior of Waspaloy during strain-controlled fatigue tests and creep tests is investigated based on the Chaboche viscoplastic model. Material parameters were determined using the least square fit to uniaxial strain-controlled low-cycle fatique and creep test results. A standard viscoplastic model using nonlinear kinematic and isotropic hardening rules gave a good description for the cyclic hardening or softening observed in symmetric low-cycle fatigue tests, but the application of the deformation model to asymmetric strain conditions resulted in a large overestimation of the mean-stress relaxation. Two modified models are presented as solutions for the overestimation of stress relaxation. A combined nonlinear and linear kinematic hardening rule (NLK+LK model) and a nonlinear kinematic hardening rule with a threshold (2-NLK-TH model) are proposed and their applications are discussed.

On the validation of the methods related to cyclic behavior of metallic structures

Abstract This work includes two ‘classical’ experimental and numerical parts. In the first part, an experimental device has been carried out and two tests have been performed on a structure subjected to a biaxial prescribed force (tension and torsion) and cyclic thermal loadings. The effect of short term mechanical overloads in tension is also analyzed with the objective to check the validity of an approach proposed previously in order to take into account that effect. The numerical part has two goals : evaluate the ability of Chaboche's viscoplastic model to describe the overloads effect and compare the assessment of some simplified methods to our experimental results. We have considered two categories of methods. The first concerns the methods based on the elastic analysis (3 Sm and efficiency rules), the second category is related to some more recent methods based on an elastic analysis combined with an elastoplastic analysis limited to the first cycle (Gatt's and Taleb's methods). The following results have been obtained: • The forecasts using the approach proposed previously in order to describe the primary overloads effect is confirmed by our tests. • The Chaboche's model has a tendency to overestimate the evolution of the strain increments induced by the successive overloads. • The predictions given by some methods based on elastic analysis (the efficiency rule in particular) do not always seem conservative. On the other hand, Gatt's and particularly Taleb's methods give some conservative forecasts for the studied cases.

Development of non‐iterative self correcting solution (NONSS) method for the viscoplastic analysis with the Chaboche model

In a finite element program for the viscoplastic analysis with Chaboche model, the non-iterative and self-correcting solution (NONSS) method, proposed by Tanaka and Miller has been implemented. Towards this, the necessary Jocobian coefficients have been derived analytically for the sopisticated 23-parameter Chaboche viscoplastic model and finally the tangent modulus matrix D* and the residual viscoplastic stress vector ξ* have been obtained in order to determine the global tangent stiffness matrix as well as pseudo-load vector. The computational efficiency of this method is demonstrated by solving a variety of bench mark problems over a wide range of rate sensitivity domain under complex monotonic and cyclic loading histories relevant to fast breeder reactor applications. An improved Self-Adaptive Eulers Forward (SAEF) method is taken as the reference for comparision. © 1998 John Wiley & Sons, Ltd.

Assessment of Life of Inner Vessel for a Pool-Type Fast Breeder Reactor Based on Inelastic and Viscoplastic Deformations

Towards assessing the creep-fatigue damage for the inner vessel of a pool-type fast reactor, 3-D elastic and axisymmetric inelastic analysis with classical kinematic hardening model, ORNL material model and more realistic CHABOCHE visco-plastic model have been performed. The material properties of stainless steel type 316 LN at various temperatures are used in the analysis. Using the results of this analysis, the creep-fatigue damage and ratcheting are assessed as per the rules of RCC-MR and results have been compared for the various constitutive models used. Inelastic analysis has been performed only at highly stressed local regions. Computations with the ORNL material model is found to be satisfactory in terms of conservatism and computer cost involved, and hence recommended for use in the design stage. Further, conservatism in estimating the creep fatigue-damage of the component associated with the elastic route of RCC-MR has been quantified. The inelastic and viscoplastic analysis tool has been validated using experimental benchmark problems.

Parameter Determination of Inelastic Constitutive Equations by Means of Neural Network.

This paper describes a new method for determining appropriate parameters of inelastic constitutive equations using the hierarchical neural network. The present method consists of three subprocesses. First, various behaviors of material under cyclic loading or creep conditions are obtained through numerical integration of constitutive equations for many combinations of their constant parameters. Each relationship between the material behaviors and the parameters is here called Next, the hierarchical neural network is trained using the learning data. Finally, the trained network is utilized to determine appropriate parameters corresponding to actual material behaviors measured in laboratory tests. To demonstrate its performance, the present method was applied to the parameter determination of Chaboche's viscoplastic model under uniaxial loading and stationary temperature conditions. The experimental data referred to are cyclic hysteresis curves of about 60 cycles and a stress relaxation curve. The results clearly show that the present method is a powerful tool for determining appropriate parameters of inelastic constitutive equations, referring to various material behaviors simultaneously.